Algorithm Design
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Algorithm Design

Algorithm Design

Algorithm Design

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828<br />

Index<br />

Mapping genomes, 279, 521 ex,<br />

787 ex<br />

Maps of routes for transportation<br />

networks, 74<br />

Margins in pretty-printing, 317-319 ex<br />

Marketing, viral, 524 ex<br />

Marking algorithms for randomized<br />

caching, 750, 752-753<br />

analyzing, 753-755<br />

notes, 794<br />

randomized, 755-758<br />

Martello, S., 335,529<br />

Matching, 337<br />

3-Dimensional Matching Problem<br />

NP-completeness, 481-485<br />

polynomial time in, 656ex<br />

problem, 481<br />

4-Dimensional Matching Problem,<br />

507 ex<br />

base-pair, 274<br />

in bipartite graphs. See Bipartite<br />

Matching Problem<br />

in load balancing, 638<br />

Minimum-Cost Perfect Matching<br />

Problem, 405-406<br />

algorithm design and analysis<br />

for, 405-410<br />

economic interpretation of,<br />

410-411<br />

notes, 449<br />

in packet switching, 798, 801-803<br />

in sequences, 278-280<br />

in Stable Matching Problem. See<br />

Stable Matching Problem<br />

Mathews, D. H., 335<br />

Matrices<br />

adjacency, 87-89<br />

entries in, 428 ex<br />

in linear programming, 631-632<br />

Matroids, 207<br />

MAX-3 -SAT<br />

algorithm design and analysis for,<br />

725-726<br />

good assignments for, 726-727<br />

notes, 793<br />

problem, 724-725<br />

random assignment for, 725-726,<br />

787 ex<br />

Max-Flow Min-Cut Theorem,<br />

348-352<br />

for Baseball Elimination Problem,<br />

403<br />

for disjoint paths, 376-377<br />

good characterizations via, 497<br />

with node capacities, 420-421 ex<br />

Maximum 3-Dimensional Matching<br />

Problem, 656 ex<br />

Maximum, computing in linear time,<br />

48<br />

Maximum-Cut Problem in local<br />

search, 676, 683<br />

algorithms for<br />

analyzing, 677-679<br />

designing, 676-677<br />

for graph partitioning, 680-681<br />

Maximum Disjoint Paths Problem,<br />

624<br />

greedy approximation algorithm<br />

for, 625-627<br />

pricing algorithm for, 628-630<br />

problem, 624-625<br />

Maximum-Flow Problem<br />

algorithm for<br />

analyzing, 344-346<br />

designing, 340-344<br />

extensions, 378-379<br />

circulations with demands,<br />

379-382<br />

circulations with demands and<br />

lower bounds, 382-384<br />

with node capacities, 420-421 ex<br />

notes, 448<br />

problem, 338-340<br />

Maximum Matching Problem. See<br />

Bipartite Matching Problem<br />

Maximum spacing, clusterings of,<br />

158-159<br />

Maximum-Weight Independent Set<br />

Problem<br />

using tree decompositions, 572,<br />

580-584<br />

on trees, 560-562<br />

Maze-Solving Problem, 78-79<br />

McGeoch, L. A., 794<br />

McGuire, C. B., 706<br />

McKeown, N., 799<br />

Median-finding, 209,727<br />

algorithm for<br />

analyzing, 730-731<br />

designing, 728-730<br />

approximation for, 791 ex<br />

problem, 727-728<br />

Medical consulting firm, 412-414ex,<br />

425-426 ex<br />

Mehlhorn, K., 71<br />

Memoization, 256<br />

over subproblems, 258-260<br />

for Weighted Interval Scheduling<br />

Problem, 256-257<br />

Memory hierarchies, 131-132<br />

Menger, K., 377, 449<br />

Menger’s Theorem, 377<br />

Merge-and-Count algorithm, 223-225<br />

Mergesort <strong>Algorithm</strong>, 210-211<br />

as example of general approach,<br />

211-212<br />

notes, 249<br />

running times for, 50-51<br />

recurrences for, 212-214<br />

Merging<br />

inversions in, 22!-225<br />

sorted lists, 48-50<br />

Meta-search tools, 222<br />

Metropolis, N., 666, 705<br />

Metropolis algorithm, 666-669<br />

Meyer, A., 543, 551<br />

Miller, G., 598<br />

Minimum-altitude connected<br />

subgraphs, 199 ex<br />

Minimum-bottleneck spanning trees,<br />

192 ex<br />

Minimum Cardinality Vertex Cover<br />

Problem, 793 ex<br />

Minimum-Cost Arborescence<br />

Problem, 116, 177<br />

greedy algorithms for<br />

analyzing, 181-183<br />

designing, 179-181<br />

problem, 177-179<br />

Minimum-Cost Dominating Set<br />

Problem, 597ex<br />

Minimum-Cost Path Problem. See<br />

Shortest Path Problem<br />

Minimum-Cost Flow Problem, 449<br />

Minimum-Cost Perfect Matching<br />

Problem, 405-406<br />

algorithm design and analysis for,<br />

405-410<br />

economic interpretation of, 410-411<br />

notes, 449<br />

Minimum cuts<br />

in Baseball Elimination Problem,<br />

403-404<br />

g!obal, 714<br />

algorithm analysis for, 716-718<br />

algorithm design for, 715-716<br />

number of, 718-719<br />

problem, 714-715<br />

in image segmentation, 393<br />

Karger’s algorithm for, 790 ex<br />

in local search, 684<br />

in Maximum-Flow Problem, 340<br />

in networks, 346<br />

algorithm analysis for, 346-348<br />

maximum flow with, 348-352<br />

notes, 793<br />

in Project Selection Problem,<br />

397-399<br />

Minimum Spanning Tree Problem,<br />

116<br />

greedy algorithms for ¯<br />

analyzing, 144-149<br />

designing, 143-144<br />

extensions, 150-151<br />

notes, 206<br />

problem, 142-143<br />

Minimum spanning trees<br />

for clustering, 157-159<br />

membership in, 188 ex<br />

Minimum-weight Steiner trees,<br />

204 ex, 335ex<br />

Minimum Weight Vertex Cover<br />

Problem, 793 ex<br />

Mismatch costs, 280<br />

Mismatches in sequences, 278-280<br />

Mitzeumacher, M., 793-794<br />

Mobile computing, base stations for,<br />

4!7-418 ex<br />

Mobile robots, 104-106 ex<br />

Mobile wireless networks, 324-325 ex<br />

Mod 2 linear equations, 779-782 ex<br />

Modified Qnicksort algorithm,<br />

732-734<br />

Molecules<br />

closest pair of points in, 226<br />

entropy of, 547-550 ex<br />

protein, 651-652 ex<br />

RNA, 273-274<br />

Monderer, D., 706<br />

Monitoring networks, 423-424 ex<br />

Monotone formulas, 507 ex<br />

Monotone QSAT, 550 ex<br />

Monotone Satisfiability, 507 ex<br />

Morse, Samuel, 163<br />

Morse code, 163<br />

Most favorable Nash equilibrium<br />

solutions, 694-695<br />

Motwani, R., 793-794<br />

Multi-phase greedy algorithms, 177<br />

analyzing, 181-183<br />

designing, 179-181<br />

problem, 177-179<br />

Multi-way choices in dynamic<br />

programming, 261<br />

algorithm for<br />

analyzing, 266<br />

designing, 264-266<br />

problem, 261-264<br />

for shortest paths, 293<br />

Mniticast, 690<br />

Mniticommodity Flow Problem, 382<br />

Multigraphs in Contraction<br />

<strong>Algorithm</strong>, 715<br />

Multiple Interval Scheduling, 512 ex<br />

Multiplication<br />

integer, 209, 231<br />

algorithm analysis for, 233-234<br />

algorithm design for, 232-233<br />

notes, 250<br />

problem, 231-232<br />

polynomials via convolution, 235,<br />

238-239<br />

Multivariable Polynomial<br />

Minimization Problem,<br />

520 ex<br />

Mutual teachability, 98-99<br />

Mutually reachable nodes, 98-99<br />

N<br />

N-node trees, 78<br />

Nabokov, Vladimir, 107 ex<br />

N~er, S., 71<br />

Nash, John, 692<br />

Nash equilibria<br />

definitions and examples, 691-693<br />

finding, 696-700<br />

notes, 706<br />

problem, 690-691<br />

questions, 695-696<br />

National Resident Matching Problem,<br />

3, 23-24 ex<br />

Natural brute-force algorithm, 31-32<br />

Natural disasters, 419 ex<br />

Nau, Dana, 552<br />

Near-trees, 200 ex<br />

Nearby Electromagnetic Observation<br />

Problem, 512-513 ex<br />

Needieman, S., 279<br />

Index 829<br />

Negation with Boolean variables, 459<br />

Negative cycles, 301<br />

algorithms for<br />

designing and analyzing,<br />

302-304<br />

extensions, 304-307<br />

in Minimum-Cost Perfect Matching<br />

Problem, 406<br />

problem, 301-302<br />

relation to shortest paths, 291-294<br />

Neighborhoods<br />

in Hopfield neural networks, 677<br />

in Image Segmentation Problem,<br />

682<br />

in local search, 663-664, 685-687<br />

in Maximum-Cut Problem, 680<br />

Nemhauser, G. L., 206<br />

Nesetril, J., 206<br />

Nested loops, running time of, 51-53<br />

Nesting arrangement for boxes,<br />

434-435 ex<br />

Network design, in Minimum<br />

Spanning Tree Problem,<br />

142-143, 150<br />

Network flow, 337-338<br />

Airline Schedufing Problem, 387<br />

algorithm analysis for, 390-391<br />

algorithm design for, 389-390<br />

problem, 387-389<br />

Baseball Elimination Problem, 400<br />

algorithm design and analysis<br />

for, 402-403<br />

characterization in, 403-404<br />

problem, 400-401<br />

Bipartite Matching Problem, See<br />

Bipartite Matching Problem<br />

Disjoint Paths Problem, 373-374<br />

algorithm analysis for, 375-377<br />

algorithm design for, 374-375<br />

algorithm extensions for,<br />

377-378<br />

problem, 374<br />

good augmenting paths for, 352<br />

algorithm analysis for, 354-356<br />

algorithm design for, 352-354<br />

algorithm extensions for,<br />

356-357<br />

finding, 412 ex<br />

Image Segmentation Problem,<br />

391-392<br />

algorithm for, 393-395

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